Quasinormal mode frequencies of Kerr black holes from Regge trajectories

Abstract

A large portion of the studies concerning the quasinormal mode frequencies of a Kerr black hole have focused only on achieving higher numerical accuracy with limited emphasis on providing their physical interpretation. In this article, we partially address this issue by computing the quasinormal mode frequency spectrum of a Kerr black hole using the theory of Regge poles. By considering the retarded Green's function of the Teukolsky equation, we establish for scalar, electromagnetic and gravitational perturbations an equation linking the Regge poles to the quasinormal frequencies and we solve it in the high-frequency regime to get "semiclassical" relations permitting us to obtain the complex frequencies of the weakly damped quasinormal modes from the Regge trajectories. Numerical results concerning gravitational perturbations ($s=-2$) are displayed. They are in excellent agreement with the "exact" ones in the eikonal regime $(\ell \gg 1)$ and in very good agreement even for lower values of $\ell$. Moreover, the splitting of each Regge pole of the Schwarzschild black hole into an infinite number of Kerr Regge poles explains the breaking of the azimuthal degeneracy of the quasinormal frequencies of the Schwarzschild black hole due to rotation. Our work is a first step to extend to Kerr black holes the approach developed for static spherically symmetric black holes which allowed, from a geometrical interpretation of the Regge poles in terms of the properties of the unstable circular null geodesics lying on the photon sphere, to derive accurate analytical formulas for the Regge trajectories and, as a by-product, for the complex frequencies of the weakly damped quasinormal modes.

References in corpus (40)

• Quasinormal modes of black holes and black branes
• Quasinormal modes of black holes: from astrophysics to string theory
• Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach
• Testing the no-hair theorem with GW150914
• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
• Black hole ringdown: the importance of overtones
• Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
• The Kerr Metric
• Universality of high-energy absorption cross sections for black holes
• Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown
• A detailed study of quasinormal frequencies of the Kerr black hole
• Gravitational perturbations of the Kerr geometry: High-accuracy study
• Can the EHT M87 results be used to test general relativity?
• Classes of Exact Solutions to the Teukolsky Master Equation
• Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation
• Branching of quasinormal modes for nearly extremal Kerr black holes
• Quasinormal modes of maximally charged black holes
• Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes
• Post-Kerr black hole spectroscopy
• Multi-mode black hole spectroscopy
• Quasinormal modes of nearly extreme Reissner-Nordstrom black holes
• Superradiance -- the 2020 Edition
• Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis
• Quasinormal modes of Kerr-de Sitter black holes via the Heun function
• Regge poles of the Schwarzschild black hole: a WKB approach
• High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation
• Asymptotics of Quasi-normal Modes for Multi-horizon Black Holes
• Regge pole description of scattering of scalar and electromagnetic waves by a Schwarzschild black hole
• The detection of Quasinormal Mode of Pop III Binary Black Hole merger with final $M\sim 60M_{\odot }$ and $a/M\sim 0.7$ would confirm the strong gravity space-time around $\sim 2M$ which is only $\sim 1.17$ times the event horizon radius
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• Modes of the Kerr geometry with purely imaginary frequencies
• Regge pole description of scattering of gravitational waves by a Schwarzschild black hole
• Scattering from compact objects: Regge poles and the complex angular momentum method
• An alternative description of gravitational radiation from black holes based on the Regge poles of the $\mathcal{S}$-matrix and the associated residues
• High-order tail in Kerr spacetime
• Quasinormal modes of the BTZ black hole are generated by surface waves supported by its boundary at infinity
• High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency
• Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails
• Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description

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